A note on degenerate Bell numbers and polynomials

TL;DR

This paper explores the properties and identities of degenerate Bell numbers and polynomials, establishing new relations and using composita to deepen understanding of these mathematical objects.

Contribution

It introduces new identities and properties of degenerate Bell polynomials, connecting them with other special polynomials and numbers, expanding the theoretical framework.

Findings

Derived new identities for degenerate Bell numbers and polynomials

Established relations between degenerate Bell polynomials and other special polynomials

Analyzed properties using the concept of composita

Abstract

Recently, several authors have studied the degenerate Bernoulli and Euler polynomials and given some intersting identities of those polynomials. In this paper, we consider the degenerate Bell numbers and polynomials and derive some new identities of those numbers and polynomials associated with special numbers and polynomials. In addition, we investigate some properties of the degenerate Bell polynomials which are derived by using the notion of composita. From our investigation, we give some new relations between the degenerate Bell polynomials and the special polynomials.